Experimental approach to Probability

Q.

A spinner has $4$ equal sectors colored yellow, blue, green and red. After spinning the spinner, what is the probability of landing on yellow color?

1. $\frac{2}{5}$

2. $\frac{1}{2}$

3. $\frac{1}{3}$

4. $\frac{1}{4}$

Q. When a die is thrown, what is the probability of getting the number 7?

1. $\frac{1}{6}$
2. $0$
3. $\frac{1}{2}$
4. $1$

Q.

A tyre manufacturing company kept a record of the distance covered before a tyre needed to be replaced. The table shows the results of $1000$ cases. If a tyre is bought from this company, what is the probability that : it has to be substituted before $4000km$ is covered?

Distance(in km)	Less than $4000$	$4000to9000$	$9001to14000$	More than $14000$
Frequency	$20$	$210$	$325$	$445$

Q.

A coin is tossed 700 times and we get head 385 times and tail 315 times. Find the probability of getting a head.

1. $\frac{315}{700}$

2. 1

3. 0

4. $\frac{11}{20}$

Q.

At a car park there are 100 vehicles, 60 of which are cars, 30 are vans and the remaining are lorries. If every vehicle is equally likely to leave, find the probability of a van leaving first.

1. 

2. 

3. 

4. 

Q.

Give me some examples of use of probability in daily life?

Q. A bag contains 9 red and 6 blue balls. Find the probability that a ball d​rawn from a bag at random is red ball.

1. $\frac{15}{15}$
2. $1$
3. $\frac{6}{15}$
4. $\frac{3}{5}$

Q.

A jar contains black and white marbles. If the probability of selecting a black marble is 0.34, then what is the probability of selecting a white marble?

1. 0.66

2. 0.58

3. 0.69

4. 0.72

Q.

A coin was tossed 1500 times and out of these, 100 times, the coin stuck somewhere so the result was not counted. The frequency of occurrence of a head was 700. Find the probability of occurrence of a tail.

1. 0.5

2. 0.3

3. 0.46

4. 1

Q.

The attendance report of a class for 150 days is as follows:

$\begin{array}{cc}\text{Student}& \text{Attendance}\\ 1& 146\\ 2& 142\\ 3& 147\\ 4& 149\\ 5& 146\\ 6& 145\\ 7& 147\\ 8& 146\\ 9& 145\\ 10& 150\\ 11& 143\\ 12& 145\\ 13& 144\\ 14& 142\\ 15& 148\end{array}$

What is the probability that a student has 98% or more attendance?

1. $\frac{1}{3}$

2. $\frac{1}{4}$

3. $\frac{1}{5}$

4. $\frac{1}{2}$

Q.

There are 10 good shirts and 5 defective shirts in a box of 15 shirts. What is the probability of finding a defective shirt?

1. $\frac{1}{10}$

2. $\frac{1}{2}$

3. $\frac{1}{3}$

4. $\frac{1}{5}$

Q.

If your current age is 10, then the probability of you turning 11 on your next birthday is .

1. 0.1

2. 3

3. 0

4. 1

Q.

1500 families with 2 children were selected randomly, and the following data were recorded:

$\begin{array}{cccc}\text{Number of girls in a family}& 2& 1& 0\\ \text{Number of families}& 300& 500& 700\end{array}$

Compute the probability of a family chosen at random having 2 girls.

1. $\frac{1}{5}$

2. $\frac{7}{15}$

3. $\frac{1}{3}$

4. $\frac{8}{15}$

Q.

Experimental or Empirical Probability of an event lies between

1. 0 and 1

2. 1 and 1.5

3. 1.5 and 2

4. 0 and 3

Q. Question 4
Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:
$$\begin{array}{ccccc}Outcome& 3heads& 2heads& 1head& Nohead\\ Frequency& 23& 72& 77& 28\end{array}$$
If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.

Q.

It is 82% likely that India will win the match means that

1. There is 100% chance that India will win

2. There is 18% chance for India to lose the match. So India will definitely not win

3. There is 82% chance that India will win. So India will certainly win

4. There is 82% chance that India will win but we cannot say that India will definitely win

Q.

^{_{​​​​​​​​​​}​​​​​​In a game a fair coinis tossed. A person is paid ₹5 if he gets head and he pays ₹2 if he gets tail . Find the probability of winning ₹5 .}

^​​​​

Q.

A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is $\frac{2}{3}$. Find the number of blue marbles in the jar.

1. 12

2. 16

3. 8

4. 11

Q.

There are 5 green, 6 black and 7 white balls in a bag. A ball is drawn at random from the bag. Find the probability that it is not white.

1. $\frac{11}{18}$

2. $\frac{7}{18}$

3. $\frac{2}{3}$

4. $\frac{5}{18}$

Q.

A die is thrown 1000 times with the frequencies for the outcomes 1, 2, 3, 4, 5 and 6 as given in the following table:

$\begin{array}{ccccccc}\text{Outcome}& 1& 2& 3& 4& 5& 6\\ \text{Frequency}& 165& 175& 180& 150& 145& 185\end{array}$

What is the probability of getting a 2 or 4?

1. 0.515

2. 0.245

3. 0.325

4. 0.455

Q.

From a set of 17 cards, numbered 1, 2, ..., 17, one card is drawn at random. What is the probability that number on the drawn card is a multiple of 3 or 7 ?

1. $\frac{7}{17}$

2. $\frac{8}{17}$

3. $\frac{6}{17}$

4. $\frac{5}{17}$

Q. What is the probability of getting 3 heads when 3 unbiased coins are tossed simultaneously?

1. $\frac{2}{5}$
2. $\frac{1}{5}$
3. $\frac{1}{8}$
4. $\frac{3}{8}$

Q.

An event is performed to throw a die and get an odd number on it. The list of favorable possible outcomes are:

1. $(1,3and5)$

2. $(2,4and6)$

3. $(1,2and6)$

4. $(1,3and6)$

Q.

A die is thrown 325 times. The frequency of the outcomes of the event 1, 2, 3, 4, 5 and 6 are recorded in the following frequency distribution table.

$\begin{array}{ccccccc}\text{Outcome}& 1& 2& 3& 4& 5& 6\\ \text{Frequency}& 50& 65& 45& 34& 55& 76\end{array}$

Find the probability of the occurrence of an (i) even number (ii) odd number.

1. $\frac{7}{13}$ and $\frac{6}{13}$

2. $\frac{11}{20}$ and $\frac{6}{13}$

3. $\frac{7}{13}$ and $\frac{8}{11}$

4. $\frac{11}{25}$ and $\frac{7}{10}$

Q.

A die is thrown 500 times and the outcomes 1, 2, 3, 4, 5, 6 have frequencies as given below

$\begin{array}{ccccccc}\text{Outcome}& 1& 2& 3& 4& 5& 6\\ \text{Frequency}& 75& 85& 90& 80& 75& 95\end{array}$

What is the probability of getting a value greater than or equal to 4?

1. 0.34

2. 0.5

3. 2

4. 0.68